They are - there is a slight difference between them , the pronoun in dativ ( we have residues of that in pronouns ) adds the meaning of 'in favor of', or in this case, 'at someone's disadvantage'.
The meaning is very easy to understand if you think of "buying" :
" Voglio comprare un libro" / " Voglio comprarmi un libro"
Now, with "comprare" you are adding a crucial piece of information with that "mi" - you are buying the book for yourself, not for somebody else.
With other verbs, such as "mangiare", "bere" , it is obvious that you are eating , drinking etc for yourself, not on behalf of somebody else, but still the "mi" emphasizes your direct interest in the matter, so to say.
This emphasis is more colloquial than the 'plain' construction - "ho mangiato una pizza" is what you would say to someone you are on formal terms with, with "mi sono mangiato una pizza" you are being somewhat more personal.
Thank you, both, for your help and quick responses! Both explanations are very clear and I have seen in the past those examples like "compro" and "mi compro." The difficulty (at least for me!) is figuring out when some of these verbs take on a completely different meaning when they become reflexive or if they simply, as you both said, reinforce a more "personal touch" to the sentence.